Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance (2019)

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K-1 Appendix K. Unbound Base Course Subroutine for Rigid Pavements The base course subroutine can calculate the stress state in the middle of base course and on the concrete/base interface. It will also calculate the suction in the middle of base course and on the interface. The outputs of the base course subroutine will be the modulus of base course, shear strength, and faulting. These will be supplied as inputs to the pavement structure model that includes interfacial degree of bonding and slab-base equivalent thickness model. The products of the equivalent thickness subroutine and the base course subroutine will be used for performance predictions of rigid pavements. The base subroutine outputs the models including:  Equilibrium suction model.  SWCC model.  Resilient modulus model for base course.  Shear strength.  Faulting models. Models of equilibrium suction, SWCC, and resilient modulus of base course for rigid pavements subroutines are the same as in unbound base course subroutine for flexible pavements in Appendix J. There is no need for the redundant repetition. The moisture-sensitive shear strength model for unbound materials is given as: ′ (K.1) where is the shear strength; is the normal stress; ′ is the effective cohesion; ′ is the effective friction angle; is the volumetric water content; is the saturation factor; and is the matric suction. Table K.1 presents the inputs to the shear strength model. Table K.1. Input Variables into Shear Strength Model. Input variables Description Unit saturated volumetric water content % OMC Optimum moisture content % PI plasticity index Gs specific gravity Two faulting models were developed to estimate the development of faulting over time and traffic repetitions, respectively. One is to predict the entire faulting development over time. This model of the full faulting curve shows that there is an inflection point in the faulting curve. Before reaching the inflection point, the accumulation of faulting is caused by the permanent deformation of the supporting layers. The formulation of the first faulting prediction model is expressed as: ln (K.2)

K-2 where is the faulting depth; is the number of days after pavement construction date. is the number of days when faulting initiates; is the number of days to failure due to erosion; and and are model coefficients. Table K.2 presents the inputs to the first faulting model parameters. Table K.2. Input Variables into First Faulting Prediction Model Parameters. Input variables Description Unit a dummy variable for the use of dowels (No dowel = 0, dowel = 1) bound a dummy variable (bound = 1 for bound base layer; bound = 0 for unbound base layer) drainage dummy variable for the use of drainage features (No drainage = 1, drainage = 1) WF, WNF, DF WF is a dummy variable (wet freeze zone = 1, else = 0); WNF is a dummy variable (wet non freeze zone = 1, else = 0); and DNF is a dummy variable (dry non freeze zone = 1, else = 0). Note that in the DF zone the dummy variables of WF, WNF, and DNF should be equal to zero. basethick base course thickness in FT freeze-thaw cycle that is number of days in the period when the air temperature goes from less than 0°C to greater than 0°C days days32C the annual average number of days with the maximum temperature greater than 32°C days wetdays the annual average number of days with precipitation greater than 0.25 mm days intensedays annual average number of days with precipitation greater than 12.7 mm days After passing the inflection point, faulting accelerates due to the action of erosion. The second model is to predict the faulting depth below the inflection point with traffic and expressed as: (K.3) 2 √3 3 (K.4) 6 √3 3 (K.5) where is the total faulting depth; is the cumulative number of axles at axle load level ; is the number of the axle when faulting occurs; is atmospheric pressure, 101.305 kPa; is the second invariant of the deviatoric stress tensor at stress level ; is the first invariant of the

K-3 stress tensor at stress level ; and , , , and are model coefficients. Table K.3 presents the inputs to the second faulting prediction model parameters. Table K.3. Input Variables into Second Faulting Prediction Model Parameters. Input variables Description Unit a dummy variable for the use of dowels (No dowel = 0, dowel = 1) bound a dummy variable (bound = 1 for bound base layer; bound = 0 for unbound base layer) WF, WNF, DF WF is a dummy variable (wet freeze zone = 1, else = 0); WNF is a dummy variable (wet non freeze zone = 1, else = 0); and DNF is a dummy variable (dry non freeze zone = 1, else = 0). Note that in the DF zone the dummy variables of WF, WNF, and DNF should be equal to zero. basethick base course thickness in FT freeze-thaw cycle that is number of days in the period when the air temperature goes from less than 0°C to greater than 0°C days days32C the annual average number of days with the maximum temperature greater than 32°C days days0C the annual average number of days with the temperature lower than 0°C days FI calculated freezing index for year (it can be collected from LTPP table of CLM_VWS_TEMP_ANNUAL).